1

Kinetics – time dependence of transformation rate

2

Kinetics of Solid-State Reactions

• Most reactions involve impedance– Formation of a new phase

– Composition different from parent

– Atomic rearrangement via diffusion required

– Energy increase at new boundaries

• Processes in microstructural transformation – Nucleation is first process in phase transformation

– Occurs at imperfection sites, grain boundaries

– Growth (until equilibrium)

3

Typical kinetic behavior for most solid-state reactions

4

Fraction of transformation (Avrami equation)

)exp(1 nkty

Rate of transformation

5.0

1

tr

5

For most reactions rate increases with temperature:

RTQAer /

6

Isothermal Transformation Diagrams (Pearlite)

(0.76 wt% C) (0.022 wt% C)+Fe3C(6.70 wt% C)

• Upon cooling (intermediate carbon content) transforms to (much lower carbon content) and Fe3C (much high carbon content)

• Pearlite = + Fe3C

cooling

heating

7

8

Pearlite (Eutectoid Composition) Reaction v. Log of Time

Temperature kept constant throughout course of experiment

9

More Convenient Analysis

Only valid foreutectoid composition

10

Note from Figure 11.4

• Derived from series of S-curves• Plot of temperature (y-axis ) v. log time in seconds

(x-axis)• Austenite transformation only upon cooling below

eutectoid temperature• Beginning curve, 50% transformation, and

completion curve• Austenite to left: pearlite to right• Start and finish curves are nearly parallel, and

they approach eutectic line asymptotically

11

Reaction Rate

• At temperature just below eutectic line rate is very slow• Apparent contradiction to r = Ae-Q/RT – increase in temperature

causes increase in rate of reaction• Between about 540 0C and 727 0C – transformation is controlled

by pearlite nucleation• Nucleation rate decreases with rising temperature (less

supercooling)• Activation energy (Q) of nucleation increases with temperature• But, at lower temperatures austenite decomposition –

transformation is diffusion controlled (as predicted by equation 11.3)

5.0

1tr

12

Isothermal Transformation Diagram(Time–Temperature–Transformation, T-T-T)

Very rapid cooling (AB)

Isothermal (BCD)

C (3.5s is beginning)

D (15s is completion)

13

Compute the mass fractions of ferrite and cementite in pearlite

14

This problem asks that we compute the mass fractions of ferrite and cementite in pearlite. The lever-rule expression for ferrite is

And, since = 6.70 wt% C, Co = 0.76 wt% C, and C = 0.022 wt% C

Similarly, for cementite

3

3

Fe C o

Fe C

C CW

C C

3Fe CC

6.70 0.760.89

6.70 0.022W

3

3

0.76 0.0220.11

6.70 0.022o

Fe CFe C

C CW

C C

15

16

17

Morphology of Pearlite

• Ferrite to cementite (approximately 8:1)• At temperature just below eutectoid –

relatively thick and Fe3C layers (coarse pearlite)

• Diffusion rates are relatively high and carbon diffuses over long distances

• With decreasing temperature, carbon diffusion rate decreases and layers become thinner (fine pearlite)

18

19

Bainite – another product of austenite transformation

• Needles or plates – needles of ferrite separated by elongated particles of the Fe3C phase

• Bainite forms as shown on the T-T-T diagram at temperatures below those where pearlite forms

• Pearlite forms – 540 to 727 0C• Bainite forms – 215 to 540 0C• Bainite and pearlite are competitive with each other – once

some portion of an alloy is transformed to either pearlite or bainite, transformation to the other microconstituent is not possible without reheating to form austentite

• Unlike pearlite – kinetics of bainite obey Arrhenius equiation – why?

20

21

Maximum rate of transformation

Pearlite – nucleationcontrolled

Bainite – diffusion controlled

22

Spheroidite

• Steel alloy having either pearlite or bainite microstructure heated to and left at a temperature below eutectic line for long period of time (18 to 24h)

• Microstructure formed is sphere like particles embedded in a continuous -phase

• Transformation due to additional carbon diffusion with no change in composition

• Driving force- reduction of -Fe3C boundary line

23

24

Martensite

• Formed when austenite cools rapidly (or is quenched) to a relatively low temperature (near ambient) – instantaneous

• Diffusionless transformation of austenite • Competitive with pearlite and banite• Occurs when quenching rate is rapid enough to

prevent carbon diffusion• Must be formed from austenite; cannot be

formed from pearlite or bainite

25

Martensite, (cont’d)

• FCC austenite experiences polymorphic transformation to BCT – diffusionless transformation from austentite – almost instantaneous since not dependent on diffusion

• Martensite structure typically maintained indefinately at room temperatures

• Supersaturated solid solution capable of rapidly transforming to other structures if heated to temperatures at which diffusion rates become appreciable

26

Needle-shaped Portion is Martensite –Rest is austensite

Martensite does not appear on iron-richphase diagram because it is metastable

27

• Martensite shown on isothermal transformation diagram

• Independent of time – not depicted in the same way as pearlite or bainite

• Function of temperature -temperature must be low enough to make carbon diffusion virtually nonexistant

• Presence of alloying elements other than carbon cause significant changes in positions and shapes of curves including shifting to longer times and formation of a separate bainite nose

28

(a) Rapidly cool to 350C, hold for 10,000s, and quench to RT

(b) Rapidly cool to 250C, holdfor 100s, and quench to RT

(c) Rapidly cool to 650C, hold for20s, rapidly cool to 400C, holdFor 1,000s, and quench to RT

29

Mechanical Properties of Pearlite

• Fe3C is harder and more brittle than ferrite

• Increasing Fe3C content increases hardness

• Fine pearlite is harder and stronger than coarse pearlite– Greater Fe3C boundary are per unit volume

– Phase boundaries serve as barriers to dislocation motion

– Fine pearlite has more boundaries through which a dislocation must pass during plastic deformation

• Coarse pearlite – more ductile than fine pearlite

30

31

32

Spheroidite

• Less boundary area

• Plastic deformation not constrained

• Ductile

• tough

33

Bainite

• Fine structure (smaller and Fe3C particles than pearlite

• Stronger and harder than pearlite

• Combination of strength and ductility

34

Martensite

• Hardest and strongest

• Most brittle

• Strength and hardness not related to microstructure – attributed to interstitial carbon atoms hindering dislocation motion

35

36

Tempered Martensite

• Martensite is so brittle that its utility is limited• Ductility and toughness may be enhanced by relieving

internal stresses by heat tempering– Heat to below eutectoid– Matensite (BCT, single phase) tempered martensite ( +

Fe3C phases)– Forms structure similar to spherodite expect cementite

particles are smaller – Large ferrite phase boundary area around very fine and

numerous cementite particles– Increasing cementite particle size decreases boundary area

and thus results in softer, weaker materail

37

38

Polymer Crystallization

• Upon cooling through melting temperature, nuclei form wherein small regions of tangled and random molecules become ordered and align in the manner of chain-folded layers

• Nuclei grow by the continued ordering and alignment of additional molecular chain segments

• Crystallization rate obeys Avrami equation:– Y = 1 – exp (-ktn)

39

40